Disjoint-union partial algebras

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are defined. We provide a recursive first-order axiomatisation of the class of partial algebras isomorphic to a disjoint-union partial algebra of sets but prove that no finite axiomatisation exists. We do the same for other signatures including one or both of disjoint union and subset complement, another partial binary operation we define. Domain-disjoint union is a partial binary operation on partial functions, returning the union if the arguments have disjoint domains and undefined otherwise. For each signature including one or both of domain-disjoint union and subset complement and optionally including composition, we consider the class of partial algebras isomorphic to a collection of partial functions closed under the operations. Again the classes prove to be axiomatisable, but not finitely axiomatisable, in first-order logic. We define the notion of pairwise combinability. For each of the previously considered signatures, we examine the class isomorphic to a partial algebra of sets/partial functions under an isomorphism mapping arbitrary suprema of pairwise combinable sets to the corresponding disjoint unions. We prove that for each case the class is not closed under elementary equivalence. However, when intersection is added to any of the signatures considered, the isomorphism class of the partial algebras of sets is finitely axiomatisable and in each case we give such an axiomatisation.Comment: 30 page

Beyond the Text: Digital Editions and Performance

Brett D. Hirsch and Janelle Jenstad, “Beyond the Text: Digital Editions and Performance.” Shakespeare Bulletin 34.1 (2016): 107–27

Moving Targets: Constructing Canons, 2013-2014

This review essay considers early modern dramatic authorship and canons in the context of two recent publications: an anthology of plays -- William Shakespeare and Others: Collaborative Plays (2013), edited by Jonathan Bate and Eric Rasmussen as a companion volume to the RSC Complete Works -- and a monograph study -- Jeremy Lopez's Constructing the Canon of Early Modern Drama (2014)

‘A Gentle and No Jew’: The Difference Marriage Makes in The Merchant of Venice

Brett D. Hirsch, “ ‘A Gentle and No Jew’: The Difference Marriage Makes in The Merchant of Venice.” Parergon, 23.1 (2006): 119–29

Jewish Questions in Robert Wilson’s The Three Ladies of London

In the history of portraying Jews on the early modern stage, critics frequently cite Robert Wilson’s The Three Ladies of London as an anomaly. The play’s first modern editor, H.S.D. Mithal, went so far as to describe Gerontus as ‘a character sui generis’, quite unlike Marlowe’s porridge-poisoning Machiavel, Shakespeare’s knife-whetting usurer, and the devilish doctor in Selimus. This essay explores the questions raised by Wilson’s portrayal of Gerontus, paying particular attention to their critical and theatrical implications. What was understood by the term ‘Jew’ and how might Elizabethan audiences have recognized Gerontus as a Jew? Is the play really an anomaly of early modern theatre history

‘In the likeness of a Jew’: Kabbalah and The Merchant of Venice

Brett D. Hirsch, “ ‘In the likeness of a Jew’: Kabbalah and The Merchant of Venice.” The Ben Jonson Journal, 12 (2005): 119-40

‘To see the Playes of Theatre newe wrought’: Electronic Editions and Early Tudor Drama

Brett D. Hirsch, “ ‘To see the Playes of Theatre newe wrought’: Electronic Editions and Early Tudor Drama.” Early Theatre 16.2 (2013): 211-49

Three Wax Images, Two Italian Gentlemen, and One English Queen

Brett D. Hirsch, “Three Wax Images, Two Italian Gentlemen, and One English Queen.” Magical Transformations on the Early Modern English Stage. Ed. Lisa Hopkins and Helen Ostovich. Farnham: Ashgate, 2014. 155-68

The Kingdom Has Been Digitized: Electronic Editions of Renaissance Drama and the Long Shadows of Shakespeare and Print

Brett D. Hirsch, “The Kingdom Has Been Digitized: Electronic Editions of Renaissance Drama and the Long Shadows of Shakespeare and Print.” Literature Compass 8.9 (2011): 568-91

‘What are these faces?’ Interpreting Bearded Women in Macbeth

Brett D. Hirsch, “ ‘What are these faces?’ Interpreting Bearded Women in Macbeth.” Renaissance Drama and Poetry in Context: Essays for Christopher Wortham. Ed. Andrew Lynch and Anne M. Scott. Newcastle-upon-Tyne: Cambridge Scholars Press, 2008. 91-114